Yes, if this W2 has an amount in Box 1, you will need to include it with your return because it has been reported to the IRS and they will be looking to match it to your return,
You are correct, if you paid for the STD insurance after taxes, it would not be taxable to you now. In this case, your W-2 should not have an amount in Box 1. I would recommend double checking with your Employer about how the premiums were paid.....it could be that you and your Employer both paid a portion of the STD and this W2 is reporting the portion paid by your Employer (which is taxable).
Check out the TurboTax FAQ below for more details:
https://ttlc.intuit.com/replies/5706614